Background: Process data captured by computer-based assessments provide valuable insight into respondents' cognitive processes during problem-solving tasks. Although previous studies have utilized process data to analyse behavioural patterns or strategies in problem-solving tasks, the connection between latent cognitive states and their theoretical interpretation in problem solving remains unclear. Objectives: This research aims to investigate the connections between similar hidden response states and unfold respondents' transition paths in problem-solving processes. Analysing process data from the 2012 United States Programme for the International Assessment of Adult Competencies (PIAAC), this study seeks to discern patterns in problem solving among participants. Methods: The hidden Markov model was first used to uncover the hidden states based on a sequence of observed actions. Next, Gaussian graphical network analysis was employed to analyse the relationships between hidden response states. Results and Conclusions: Results indicated that correct responders had simpler, clearer state relationships, while incorrect responders displayed more complex connections. Respondents who solved the tasks correctly had clearer thoughts about the problem-solving process, whereas incorrect respondents struggled to understand the problem and failed to figure out solutions. Cognitive state changes during problem solving also varied between groups. The correct groups showed cohesive, logical transitions, in contrast to the emerged isolated, erratic patterns of the incorrect groups.